Florence had sustained wind near 50 mph Wednesday, over the 39 mph threshold for a tropical storm. National Hurricane Center forecasters said it could strengthen into a hurricane, with winds of at least 74 mph, as early as Thursday.
At 5 p.m. EDT, the storm was centered about 770 miles east of the Northern Leeward Islands, or about 1,900 miles southeast of Miami, and was moving toward the west-northwest about 9 mph.
"The concern would be Bermuda at this point, how close the destructive force winds will move toward it," said Dave Roberts, a forecaster at the hurricane center. Florence's center was about 1,240 miles southeast of Bermuda on Wednesday.
Tropical storm-force wind extended up to 260 miles from its center.
"Although Florence continues to get better organized, it remains an unusually large Atlantic tropical storm, and large cyclones tend to take longer to develop and intensify than smaller ones do," said hurricane specialist Stacy Stewart.
Florence follows on the heels of Tropical Storm Ernesto, which formed Aug. 25 over the southern Caribbean and was briefly the season's first hurricane before weakening and hitting Florida and North Carolina last week as a tropical storm.
At least nine deaths in the United States were blamed on Ernesto, which also killed two people in Haiti, delayed the launch of the space shuttle Atlantis and blacked out thousands of homes and businesses from North Carolina to New York.
Last year's Atlantic storm season had a record 28 named storms and 15 hurricanes, including Katrina.
The 2006 Atlantic hurricane season has not been as rough as initially feared. The National Hurricane Center lowered its forecast in August to between 12 and 15 named storms and seven to nine hurricanes.